Sine notes

[Jim Eshelman]

An interesting article for those not familiar with the subject. Not only does a sine wave define all major aspects (i.e., which angular separations constitute major aspects), it seems that aspect amplitude (strength) varies at a sinusoid-determined pace. Though this opinion is based on observation of aspect behavior, this article (and similar summaries by mathematicians) may show why it is also intellectually gratifying that it should be so.

Some quotes I like:

A sine wave or sinusoidal wave is the most natural representation of how many things in nature change state.

A sine wave shows how the amplitude of a variable changes with time. The variable could be audible sound for example. A single pure note is a sine wave, although it would sound a very plain and flat note indeed with none of the harmonics we normally hear in nature. A straightforward oscillating or alternating current or voltage within a wire can also be represented by a sine wave.

The sine of any angle can vary from −1 to +1. For example the sine of 0° is 0 and the sine of 90° is 1. The sine of 270° is −1 and when we get to 360° we are back to zero again.

Not only does the wave cycle from its high point +1 at -0°, through 0 at 90°, to its minimum -1 at 180°, back through zero at the closing square... it also hits +0.5 at 60° and -0.5 at 120°. The curve defines the major aspects.

[Jim Eshelman]

An inquiry on Quora of, "What is one natural phenomenon that is predictable by means of a periodic sine or cosine wave or curve?" brought the following answer from Gregory Benson, a retired research geoscientist:

The brightness of the moon through its phases.
The resonant sound of a tube horn, whistle, or reed instrument.
Alternating current.
The motion of a piston in an engine
Brain waves

To these, of course, could be added the basics that first come to mind: light waves, sound waves, and waves or tides of wind or ocean water.

All planetary orbits and other body paths of motion are conic sections that are simply more complex sinusoidal functions.

Sine-based curves are fundamental to the structure of the physical universe, including the energy patterns that constitute both the substance and the near-insubstantial fringe of the physical universe.

[Ethan FM]

Not only does the wave cycle from its high point +1 at -0°, through 0 at 90°, to its minimum -1 at 180°, back through zero at the closing square... it also hits +0.5 at 60° and -0.5 at 120°. The curve defines the major aspects.

That right there is something.

You mentioned waves, which made me think of this article I came across last week. The picture is something else and I found myself staring and staring at it... related?

https://www.nasa.gov/feature/magnetic-c ... ool-galaxy

-Ethan

[Jim Eshelman]

Whirlpools are "golden mean" (or Fibonacci) structured. These pictures might make that easier to see: https://www.bing.com/images/search?q=fi ... RE&first=1

[Ethan FM]

I think whirlpools are "golden mean" (or Fibonacci) structured. These pictures might make that easier to see: https://www.bing.com/images/search?q=fi ... RE&first=1

That makes more sense now - my brain sometimes!

-Ethan